Linkage Analysis

Handbook of Statistical Genetics: Third Edition

Volumn 2, Issue , 2008, Pages 1141-1167

  Thompson, E A ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

Complex traits linkage analysis; DNA markers; gene ordering inference; Hardy Weinberg equilibrium; Human genetic linkage analysis; Interconnected pedigree loops; Maximum likelihood estimates; Mendelian segregation and linkage relationships; Monte Carlo multipoint linkage likelihoods

Indexed keywords

EID: 52949149045     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470061619.ch33     Document Type: Chapter

References (97)

1. Abecasis, G.R., Cherny, S.S., Cookson, W.O. and Cardon, L.R. (2002) Merlin-rapid analysis of dense genetic maps using sparse gene flow trees. Nature Genetics 30, (97-101).
2. Bailey, N.T.J. (1961) Introduction to the Mathematical Theory of Genetic Linkage. Clarendon Press, Oxford.
3. Barnard, G.A. (1949) Statistical inference. Journal of the Royal Statistical Society Series B 11, (115-139).
4. Baum, L.E. (1972) An inequality and associated maximization technique in statistical estimation for probabilistic functions on Markov processes. In Inequalities-III; Proceedings of the Third Symposium on Inequalities. University of California Los Angeles, 1969, O. Shisha, ed. Academic Press, New York, pp. 1-8.
5. Baum, L.E., Petrie, T., Soules, G. and Weiss, N. (1970) A maximization technique occurring in the statistical analysis of probabilistic functions on Markov chains. Annals of Mathematical Statistics 41, (164-171).
6. Boehnke, M. (1994). Limits of resolution of genetic linkage studies: implications for the positional cloning of human disease genes. American Journal of Human Genetics 55(2), 379-390.
7. Botstein, D., White, R.L., Skolnick, M.H. and Davis, R.W. (1980) Construction of a linkage map in man using restriction fragment polymorphism. American Journal of Human Genetics 32, (314-331).
8. Browning, S. (2000) A Monte Carlo approach to calculating probabilities for continuous identity by descent data. Journal of Applied Probability 37, (850-864).
9. Cannings, C., Thompson, E.A. and Skolnick, M.H. (1978) Probability functions on complex pedigrees. Advances of Applied Probability 10, (26-61).
10. Cannings, C., Thompson, E.A. and Skolnick, M.H. (1980). Pedigree analysis of complex models. In Current Developments in Anthropological Genetics, J. Mielke and M. Crawford, eds. Plenum Press, New York, pp. 251-298.
11. Churchill, G.A. and Doerge, R.W. (1994). Empirical threshold values for quantitative trait mapping. Genetics 138(3), 963-71.
12. Cottingham, R.W., Idury, R.M. and Schäffer, A.A. (1993) Faster sequential genetic linkage computations. American Journal of Human Genetics 53, (252-263).
13. Curtis, D. and Gurling, H. (1993) A procedure for combining two-point lod scores into a summary multipoint map. Human Heredity 43, (173-185).
14. Daw, E.W., Kumm, J., Snow, G.L., Thompson, E.A. and Wijsman, E.M. (1999). MCMC methods for genome screening. Genetic Epidemiology 17(SUPPL. 1), S133-S138.
15. Daw, E.W., Thompson, E.A. and Wijsman, E.M. (2000) Bias in multipoint linkage analysis arising from map misspecification. Genetic Epidemiology 19, (366-380).
16. Dempster, A.P., Laird, N.M. and Rubin, D.B. (1977) Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society Series B 39, (1-37).
17. Donnelly, K.P. (1983). The probability that related individuals share some section of genome identical by descent. Theoretical Population Biology 23(1), 34-63.
18. Edwards, J.H. (1971) The analysis of X-linkage. Annals of Human Genetics 34, 229-259.
19. Elston, R.C. and Stewart, J. (1971). A general model for the analysis of pedigree data. Human Heredity21, (523-542).
20. Epstein, M., Duren, W. and Boehnke, M. (2000) Improved inference of relationship for pairs of individuals. American Journal of Human Genetics 67, (1219-1231).
21. Fischelson, M. and Geiger, D. (2004) Optimizing exact linkage computations. Journal of Computational Biology 11, (263-275).
22. Fisher, R.A. (1922a). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London Series A 222, 309-368.
23. Fisher, R.A. (1922b). The systematic location of genes by means of crossover observations. American Naturalist 56, 406-411.
24. Fisher, R.A. (1934) The amount of information supplied by records of families as a function of the linkage in the population sampled. Annals of Eugenics 6, (66-70).
25. Fisher, R.A. (1936) Heterogeneity of linkage data for Friedreich's ataxia and the spontaneous antigens. Annals of Eugenics 7, (17-21).
26. Fisher, R.A. (1949) The Theory of Inbreeding. Oliver and Boyd, Edinburgh.
27. Gelfand, A.E. and Smith, A.F.M. (1990) Sampling based approaches to calculating marginal densities. Journal of the American Statistical Association 85, (398-409).
28. George, A.W. and Thompson, E.A. (2003) Multipoint linkage analyses for disease mapping inextended pedigrees: a Markov chain Monte Carlo approach. Statistical Science 18, (515-531).
29. Geyer, C.J. and Thompson, E.A. (1995) Annealing Markov chain Monte Carlo with applications to ancestral inference. Journal of the American Statistical Association 90, (909-920).
30. Goldstein, D.R., Zhao, H. and Speed, T.P. (1995). Relative efficiencies of chi-square models of recombination for exclusion mapping and gene ordering. Genomics 27(2), 265-273.
31. Gretarsdottir, S., Sveinbjornsdottir, S., Jonsson, H.H., Jakobsson, F., Einarsdottir, E., Agnarsson, U., Shkolny, D., Einarsson, G., Gudjonsdottir, H.M., Valdimarsson, E.M., Einarsson, O.B., Thorgeirsson, G., Hadzic, R., Jonsdottir, S., Reynisdottir, S.T., Bjarnadottir, S.M., Gudmundsdottir, T., Gudlaugsdottir, G.J., Gill, R., Lindpaintner, K., Sainz, J., Hannesson, H.H., Sigurdsson, G.T., Frigge, M.L., Kong, A., Gudnason, V., Stefansson, K. and Gulcher, J.R. (2002) Localization of a susceptibility gene for common forms of stroke to 5q12. American Journal of Human Genetics 70, (593-603).
32. Gudbjartsson, D., Jonasson, K., Frigge, M. and Kong, A. (2000) Allegro, a new computer program for multipoint linkage analysis. Nature Genetics 25, (12-13).
33. Guo, S.W. and Thompson, E.A. (1994). Monte Carlo estimation of mixed models for large complex pedigrees. Biometrics 50(2), 417-432.
34. Haldane, J.B.S. (1919) The combination of linkage values and the calculation of distances between the loci of linked factors. Journal of Genetics 8, (229-309).
35. Haldane, J.B.S. (1934) Methods for the detection of autosomal linkage in man. Annals of Eugenics 6, (26-65).
36. Haldane, J.B.S. and Smith, C.A.B. (1947) A new estimate of the linkage between the genes for colour-blindness and haemophilia in man. Annals of Eugenics 14, (10-31).
37. Halpern, J. and Whittemore, A.S. (1999) Multipoint linkage analysis. A cautionary note. Human Heredity 49, (194-196).
38. Hartl, D.L. and Clark, A.G. (1997) Principles of Population Genetics, 3rd edition. Sinauer, Sunderland, MA. Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, (97-109).
39. Heath, S.C. (1997). Markov chain Monte Carlo segregation and linkage analysis for oligogenic models. American Journal of Human Genetics 61(3), 748-760.
40. Heath, S. and Thompson, E.A. (1997). MCMC samplers for multilocus analyses on complex pedigrees. American Journal of Human Genetics 61(SUPPL.), A278.
41. Heuch, I. and Li, F.M.H. (1972) PEDIG-A computer program for calculation of genotype probabilities, using phenotypic information. Clinical Genetics 3, (501-504).
42. Hilden, J. (1970) GENEX-An algebraic approach to pedigree probability calculus. Clinical Genetics 1, (319-348).
43. Irwin, M., Cox, N. and Kong, A. (1994) Sequential imputation for multilocus linkage analysis. Proceedings of the National Academy of Sciences of the United States of America 91, (11684-11688).
44. King, T.R., Dove, W.F., Guénet, J., Hermann, B.G. and Shedlovsky, A. (1991) Meiotic mapping of murine chromosome 17: the string of loci around l(17)-2-Pas. Mammalian Genome 1, (37-46).
45. Kong, A., Liu, J. and Wong, W.H. (1994) Sequential imputations and Bayesian missing data problems. Journal of the American Statistical Association 89, (278-288).
46. Kruglyak, L., Daly, M.J., Reeve-Daly, M.P. and Lander, E.S. (1996). Parametric and nonparametric linkage analysis: a unified multipoint approach. American Journal of Human Genetics 58(6), 1347-1363.
47. Kullback, S. and Leibler, R.A. (1951) On information and sufficiency. Annals of Statistics 22, (79-86).
48. Lander, E.S. and Botstein, D. (1987) Homozygosity mapping: a way to map human recessive traits with the DNA of inbred children. Science 236, (1567-1570).
49. Lander, E.S. and Green, P. (1987). Construction of multilocus genetic linkage maps in humans.Proceedings of the National Academy of Sciences of the United States of America 84(8), 2363-2367.
50. Lange, K. and Sobel, E. (1991) A random walk method for computing genetic location scores. American Journal of Human Genetics 49, (1320-1334).
51. Lathrop, G.M., Lalouel, J.M., Julier, C. and Ott, J. (1984) Strategies for multilocus linkage analysis in humans. Proceedings of the National Academy of Sciences of the United States of America 81, (3443-3446).
52. Lauritzen, S.L. and Spiegelhalter, D.J. (1988) Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society Series B 50, (157-224).
53. Liberman, U. and Karlin, S. (1984). Theoretical models of genetic map functions. Theoretical Population Biology 25(3), 331-346.
54. Lin, S. and Speed, T.P. (1996) Incorporating crossover interference into pedigree analysis using the χ2 model. Human Heredity 46, (315-322).
55. Liu, J., Wong, W.H. and Kong, A. (1994) A covariance struture of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika 81, (27-40).
56. McPeek, M.S. (1999) Optimal allele-sharing statistics for genetic mapping using affected relatives. Genetic Epidemiology 16, (225-249).
57. McPeek, M. and Sun, L. (2000) Statistical tests for detection of misspecified relationships by use of genome-screen data. American Journal of Human Genetics 66, (1076-1094).
58. Mendel, G. (1866). Experiments in plant hybridisation. In English Translation and Commentary by R. A. Fisher, J.H. Bennett, ed. Oliver and Boyd, Edinburgh 1965.
59. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) Equations of state calculations by fast computing machines. Journal of Chemical Physics 21, (1087-1092).
60. Morton, N.E. (1955) Sequential tests for the detection of linkage. American Journal of Human Genetics 7, (277-318).
61. Morton, N.E. and MacLean, C.J. (1974) Analysis of family resemblance.III. Complex segregation of quantitative traits. American Journal of Human Genetics 26, (489-503).
62. Murray, J.C., Buetow, K.H., Weber, J.L., Ludwigson, S., Scherpier-Heddema, T., Manion, F., Quillen, J., Sheffield, V., Sunden, S., Duyk, G.M., Weissenbach, J., Gyapay, G., Dib, C., Morrissette, J., Lathrop, G.M., Vignal, A., White, R., Matsunami, N., Gerken, S., Melis, R.,Albertsen, H., Plaetke, R., Odelberg, S., Ward, D., Dausset, J., Cohen, D. and Cann, H. (1994) A comprehensive human linkage map with centimorgan density. Science 265, (2049-2064).
63. NIH-CEPH Collaborative Mapping Group (1992). A comprehensive genetic linkage map of the human genome, Science 258, 67-86.
64. O'Connell, J.R. and Weeks, D.E. (1995). The algorithm for rapid exact multilocus linkage analysis via genotype set-recoding and fuzzy inheritance. Nature Genetics 11(4), 402-408.
65. Ott, J. (1974) Estimation of the recombination frequency in human pedigrees: efficient computation of the likelihood for human linkage studies. American Journal of Human Genetics 26, (588-597).
66. Ott, J. (1979) Maximum likelihood estimation by counting methods under polygenic and mixed models in human pedigrees. American Journal of Human Genetics 31, (161-175).
67. Ott, J. (1999) Analysis of Human Genetic Linkage, 3rd edition. The Johns Hopkins University Press, Baltimore, MD.
68. Penrose, L.S. (1935) The detection of autosomal linkage in data which consist of pairs of brothers and sisters of unspecified parentage. Annals of Eugenics 6, (133-138).
69. Ploughman, L.M. and Boehnke, M. (1989) Estimating the power of a proposed linkage study for a complex genetic trait. American Journal of Human Genetics 44, (543-551).
70. Renwick, J.H. (1969) Progress in mapping the human autosomes. British Medical Bulletin 25, (65-73).
71. Robbins, R.B. (1918) Some applications of mathematics to breeding problems.III. Genetics 3, (375-389).
72. Sieberts, S.K., Wijsman, E.M. and Thompson, E.A. (2002) Relationship inference from trios of individuals in the presence of typing error. American Journal of Human Genetics 70, (170-180).
73. Silberstein, M., Tzemach, A., Dovgolesky, N., Fishelson, M., Schuster, A. and Geiger, D. (2006) Online system for faster multipoint linkage analysis via parallel executation on thousands of personal computers. American Journal of Human Genetics 78, (922-935).
74. Skrivanek, Z., Lin, S. and Irwin, M.E. (2003) Linkage analysis with sequential imputation. Genetic Epidemiology 25, (25-35).
75. Smith, C.A.B. (1953) Detection of linkage in human genetics. Journal of the Royal Statistical Society Series B 15, (153-192).
76. Smith, C.A.B. (1963) Testing for heterogeneity of recombination fractions in human genetics. Annals of Human Genetics 27, (175-182).
77. Sobel, E. and Lange, K. (1996) Descent graphs in pedigree analysis: applications to haplotyping, location scores, and marker-sharing statistics. American Journal of Human Genetics 58, (1323-1337).
78. Stewart, W.C.L. and Thompson, E.A. (2006) Improving estimates of genetic maps: a maximum likelihood approach. Biometrics 62, (728-734).
79. Sturtevant, A.H. (1913) The linear association of six sex-linked factors in Drosophila, as shown by their mode of association. Journal of Experimental Zoology 14, (43-59).
80. Suarez, B.K., Rice, J. and Reich, T. (1978) The generalized sib pair IBD distribution: its use in the detection of linkage. Annals of Human Genetics 42, (87-94).
81. Sung, Y.J., Thompson, E.A. and Wijsman, E.M. (2006) MCMC-based multipoint linkage analysis for two loci plus a polygenic component and general pedigrees. Genetic Epidemiology 31, (103-114).
82. Thomas, A., Gutin, A. and Abkevich, V. (2000) Multilocus linkage analysis by blocked Gibbs sampling. Statistics and Computing 10, (259-269).
83. Thompson, E.A. (1974) Gene identities and multiple relationships. Biometrics 30, (667-680).
84. Thompson, E.A. (1994) Monte Carlo likelihood in genetic mapping. Statistical Science 9, (355-366).
85. Thompson, E.A. (2000). Statistical Inferences from Genetic Data on Pedigrees, Vol. 6 of NSF-CBMS Regional Conference Series in Probability and Statistics, Institute of Mathematical Statistics, Beachwood, OH.
86. Thompson, E.A. (2005). Chapter 4: MCMC in the analysis of genetic data on pedigrees. In Markov Chain Monte Carlo: Innovations and Applications, F. Liang, J.-S. Wang and W. Kendall, eds. World Scientific Co Pvt Ltd, Singapore, pp. 183-216.
87. Thompson, E.A. and Geyer, C.J. (2007) Fuzzy p-values in latent variable problems. Biometrika 94, (49-60).
88. Thompson, E.A. and Guo, S.W. (1991). Evaluation of likelihood ratios for complex genetic models. I.M.A. Journal of Mathematics Applied in Medicine and Biology 8(3), 149-169.
89. Thompson, E.A. and Heath, S.C. (1999). Estimation of conditional multilocus gene identity among relatives. In Statistics in Molecular Biology and Genetics: Selected Proceedings of a 1997 Joint AMS-IMS-SIAM Summer Conference on Statistics in Molecular Biology, IMS Lecture Note-Monograph Series, Vol. 33, F. Seillier-Moiseiwitsch, ed. Institute of Mathematical Statistics, Hayward, CA, pp. 95-113.
90. Thompson, E.A., Kravitz, K., Hill, J. and Skolnick, M.H. (1978). Linkage and the power of a pedigree structure. In Genetic Epidemiology, N.E. Morton, ed. Academic Press, New York, pp. 247-253.
91. Thompson, E.A. and Meagher, T.R. (1998) Genetic linkage in the estimation of pairwise relationship. Theoretical and Applied Genetics 97, (857-864).
92. Wald, A. (1947). Sequential Analysis. John Wiley & Sons, New York.
93. Weeks, D.E. and Lange, K. (1988) The affected pedigree member method of linkage analysis. American Journal of Human Genetics 42, (315-326).
94. Weeks, D.E., Lathrop, G.M. and Ott, J. (1993). Multipoint mapping under genetic interference. Human Heredity 43(2), 86-97.
95. Weinstein, A. (1936) The theory of multiple-strand crossing over. Genetics 21, (155-199).
96. Wijsman, E.M. and Amos, C.I. (1997) Genetic analysis of simulated oligogenic traits in nuclear and extended pedigrees: summary of GAW10 contributions. Genetic Epidemiology 14, (719-735).
97. Zhao, H., Speed, T.P. and McPeek, M.S. (1995). Statistical analysis of crossover interference using the chi-square model. Genetics 139(2), 1045-1056.